<?xml version="1.0"?>
<div class="add">

<b>reconsider </b><font color="Maroon" title="c4">F</font> = <span class="p1">(<span class="default"><a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c3">S</font>,0</span>)</span> <a href="ami_3.html#K14" title="AMI_3:func.14">.--&gt;</a> <span class="p1">(<span class="default"><a href="ami_1.html#K5" title="AMI_1:func.5">halt</a> <font color="Maroon" title="c3">S</font></span>)</span> as  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <a href="ami_3.html#V1" title="AMI_3:attr.1">programmed</a> <a href="amistd_1.html#V9" title="AMISTD_1:attr.9">lower</a>  <a href="ami_1.html#M1" title="AMI_1:mode.1">FinPartState</a> of <font color="Maroon" title="c3">S</font> <b>by </b><i><a class="ref" href="amistd_1.html#T48" target="_self" title="AMISTD_1:th.48">Th48</a></i>;<br/>
<a NAME="E2:98_1_1"/>
( <font color="Maroon" title="c4">F</font> is <a href="amistd_1.html#V10" title="AMISTD_1:attr.10">halt-ending</a> &amp; <font color="Maroon" title="c4">F</font> is <a href="amistd_1.html#V11" title="AMISTD_1:attr.11">unique-halt</a> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="98_1_1_1"><b>proof </b></a><div class="add">

<b>thus </b><a NAME="E1:98_1_1_1"/>
( <font color="Maroon" title="c4">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="amistd_1.html#K10" title="AMISTD_1:func.10">LastLoc</a> <font color="Maroon" title="c4">F</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K5" title="AMI_1:func.5">halt</a> <font color="Maroon" title="c3">S</font> &amp; ( for <font color="Olive" title="b1">l</font> being  <a href="ami_1.html#NM2" title="AMI_1:NM.2">Instruction-Location</a> of <font color="Maroon" title="c3">S</font>  st <font color="Maroon" title="c4">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">l</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K5" title="AMI_1:func.5">halt</a> <font color="Maroon" title="c3">S</font> &amp; <font color="Olive" title="b1">l</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c4">F</font> holds <br/><font color="Olive" title="b1">l</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="amistd_1.html#K10" title="AMISTD_1:func.10">LastLoc</a> <font color="Maroon" title="c4">F</font> ) )
 <b>by </b><i><a class="txt" href="amistd_1.html#E83"><i><font color="Green" title="E48">Lm7</font></i></a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="amistd_1.html#D22" target="_self" title="AMISTD_1:def.22">AMISTD_1:def 22</a>,<a class="ref" href="amistd_1.html#D23" target="_self" title="AMISTD_1:def.23">AMISTD_1:def 23</a><br/>


</div><b>end;</b></div>
<b>then reconsider </b><font color="Maroon" title="c5">F</font> = <font color="Maroon" title="c4">F</font> as   <a href="amistd_1.html#NM1" title="AMISTD_1:NM.1">pre-Macro</a> of <font color="Maroon" title="c3">S</font> ;<br/>
<b>take </b>
<font color="Maroon" title="c5">F</font>
;<br/>

<b>thus </b><a NAME="E4:98_1_1"/>
<font color="Maroon" title="c5">F</font> is <a href="amistd_1.html#V6" title="AMISTD_1:attr.6">closed</a>
 <b>by </b><i><a class="ref" href="amistd_1.html#T46" target="_self" title="AMISTD_1:th.46">Th46</a></i>;<br/>


</div>
